/*
 * Copyright (c) 1999, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
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 *
 *
 *
 *
 */

package java.lang;

import java.util.Random;
import sun.misc.DoubleConsts;

/**
 * The class {@code StrictMath} contains methods for performing basic
 * numeric operations such as the elementary exponential, logarithm,
 * square root, and trigonometric functions.
 *
 * <p>To help ensure portability of Java programs, the definitions of
 * some of the numeric functions in this package require that they
 * produce the same results as certain published algorithms. These
 * algorithms are available from the well-known network library
 * {@code netlib} as the package "Freely Distributable Math
 * Library," <a
 * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
 * algorithms, which are written in the C programming language, are
 * then to be understood as executed with all floating-point
 * operations following the rules of Java floating-point arithmetic.
 *
 * <p>The Java math library is defined with respect to
 * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
 * more than one definition for a function (such as
 * {@code acos}), use the "IEEE 754 core function" version
 * (residing in a file whose name begins with the letter
 * {@code e}).  The methods which require {@code fdlibm}
 * semantics are {@code sin}, {@code cos}, {@code tan},
 * {@code asin}, {@code acos}, {@code atan},
 * {@code exp}, {@code log}, {@code log10},
 * {@code cbrt}, {@code atan2}, {@code pow},
 * {@code sinh}, {@code cosh}, {@code tanh},
 * {@code hypot}, {@code expm1}, and {@code log1p}.
 *
 * <p>
 * The platform uses signed two's complement integer arithmetic with
 * int and long primitive types.  The developer should choose
 * the primitive type to ensure that arithmetic operations consistently
 * produce correct results, which in some cases means the operations
 * will not overflow the range of values of the computation.
 * The best practice is to choose the primitive type and algorithm to avoid
 * overflow. In cases where the size is {@code int} or {@code long} and
 * overflow errors need to be detected, the methods {@code addExact},
 * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}
 * throw an {@code ArithmeticException} when the results overflow.
 * For other arithmetic operations such as divide, absolute value,
 * increment, decrement, and negation overflow occurs only with
 * a specific minimum or maximum value and should be checked against
 * the minimum or maximum as appropriate.
 *
 * @author unascribed
 * @author Joseph D. Darcy
 * @since 1.3
 */

public final class StrictMath {

  /**
   * Don't let anyone instantiate this class.
   */
  private StrictMath() {
  }

  /**
   * The {@code double} value that is closer than any other to
   * <i>e</i>, the base of the natural logarithms.
   */
  public static final double E = 2.7182818284590452354;

  /**
   * The {@code double} value that is closer than any other to
   * <i>pi</i>, the ratio of the circumference of a circle to its
   * diameter.
   */
  public static final double PI = 3.14159265358979323846;

  /**
   * Returns the trigonometric sine of an angle. Special cases:
   * <ul><li>If the argument is NaN or an infinity, then the
   * result is NaN.
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.</ul>
   *
   * @param a an angle, in radians.
   * @return the sine of the argument.
   */
  public static native double sin(double a);

  /**
   * Returns the trigonometric cosine of an angle. Special cases:
   * <ul><li>If the argument is NaN or an infinity, then the
   * result is NaN.</ul>
   *
   * @param a an angle, in radians.
   * @return the cosine of the argument.
   */
  public static native double cos(double a);

  /**
   * Returns the trigonometric tangent of an angle. Special cases:
   * <ul><li>If the argument is NaN or an infinity, then the result
   * is NaN.
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.</ul>
   *
   * @param a an angle, in radians.
   * @return the tangent of the argument.
   */
  public static native double tan(double a);

  /**
   * Returns the arc sine of a value; the returned angle is in the
   * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
   * <ul><li>If the argument is NaN or its absolute value is greater
   * than 1, then the result is NaN.
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.</ul>
   *
   * @param a the value whose arc sine is to be returned.
   * @return the arc sine of the argument.
   */
  public static native double asin(double a);

  /**
   * Returns the arc cosine of a value; the returned angle is in the
   * range 0.0 through <i>pi</i>.  Special case:
   * <ul><li>If the argument is NaN or its absolute value is greater
   * than 1, then the result is NaN.</ul>
   *
   * @param a the value whose arc cosine is to be returned.
   * @return the arc cosine of the argument.
   */
  public static native double acos(double a);

  /**
   * Returns the arc tangent of a value; the returned angle is in the
   * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
   * <ul><li>If the argument is NaN, then the result is NaN.
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.</ul>
   *
   * @param a the value whose arc tangent is to be returned.
   * @return the arc tangent of the argument.
   */
  public static native double atan(double a);

  /**
   * Converts an angle measured in degrees to an approximately
   * equivalent angle measured in radians.  The conversion from
   * degrees to radians is generally inexact.
   *
   * @param angdeg an angle, in degrees
   * @return the measurement of the angle {@code angdeg} in radians.
   */
  public static strictfp double toRadians(double angdeg) {
    // Do not delegate to Math.toRadians(angdeg) because
    // this method has the strictfp modifier.
    return angdeg / 180.0 * PI;
  }

  /**
   * Converts an angle measured in radians to an approximately
   * equivalent angle measured in degrees.  The conversion from
   * radians to degrees is generally inexact; users should
   * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
   * equal {@code 0.0}.
   *
   * @param angrad an angle, in radians
   * @return the measurement of the angle {@code angrad} in degrees.
   */
  public static strictfp double toDegrees(double angrad) {
    // Do not delegate to Math.toDegrees(angrad) because
    // this method has the strictfp modifier.
    return angrad * 180.0 / PI;
  }

  /**
   * Returns Euler's number <i>e</i> raised to the power of a
   * {@code double} value. Special cases:
   * <ul><li>If the argument is NaN, the result is NaN.
   * <li>If the argument is positive infinity, then the result is
   * positive infinity.
   * <li>If the argument is negative infinity, then the result is
   * positive zero.</ul>
   *
   * @param a the exponent to raise <i>e</i> to.
   * @return the value <i>e</i><sup>{@code a}</sup>, where <i>e</i> is the base of the natural
   * logarithms.
   */
  public static native double exp(double a);

  /**
   * Returns the natural logarithm (base <i>e</i>) of a {@code double}
   * value. Special cases:
   * <ul><li>If the argument is NaN or less than zero, then the result
   * is NaN.
   * <li>If the argument is positive infinity, then the result is
   * positive infinity.
   * <li>If the argument is positive zero or negative zero, then the
   * result is negative infinity.</ul>
   *
   * @param a a value
   * @return the value ln&nbsp;{@code a}, the natural logarithm of {@code a}.
   */
  public static native double log(double a);


  /**
   * Returns the base 10 logarithm of a {@code double} value.
   * Special cases:
   *
   * <ul><li>If the argument is NaN or less than zero, then the result
   * is NaN.
   * <li>If the argument is positive infinity, then the result is
   * positive infinity.
   * <li>If the argument is positive zero or negative zero, then the
   * result is negative infinity.
   * <li> If the argument is equal to 10<sup><i>n</i></sup> for
   * integer <i>n</i>, then the result is <i>n</i>.
   * </ul>
   *
   * @param a a value
   * @return the base 10 logarithm of  {@code a}.
   * @since 1.5
   */
  public static native double log10(double a);

  /**
   * Returns the correctly rounded positive square root of a
   * {@code double} value.
   * Special cases:
   * <ul><li>If the argument is NaN or less than zero, then the result
   * is NaN.
   * <li>If the argument is positive infinity, then the result is positive
   * infinity.
   * <li>If the argument is positive zero or negative zero, then the
   * result is the same as the argument.</ul>
   * Otherwise, the result is the {@code double} value closest to
   * the true mathematical square root of the argument value.
   *
   * @param a a value.
   * @return the positive square root of {@code a}.
   */
  public static native double sqrt(double a);

  /**
   * Returns the cube root of a {@code double} value.  For
   * positive finite {@code x}, {@code cbrt(-x) ==
   * -cbrt(x)}; that is, the cube root of a negative value is
   * the negative of the cube root of that value's magnitude.
   * Special cases:
   *
   * <ul>
   *
   * <li>If the argument is NaN, then the result is NaN.
   *
   * <li>If the argument is infinite, then the result is an infinity
   * with the same sign as the argument.
   *
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.
   *
   * </ul>
   *
   * @param a a value.
   * @return the cube root of {@code a}.
   * @since 1.5
   */
  public static native double cbrt(double a);

  /**
   * Computes the remainder operation on two arguments as prescribed
   * by the IEEE 754 standard.
   * The remainder value is mathematically equal to
   * <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>,
   * where <i>n</i> is the mathematical integer closest to the exact
   * mathematical value of the quotient {@code f1/f2}, and if two
   * mathematical integers are equally close to {@code f1/f2},
   * then <i>n</i> is the integer that is even. If the remainder is
   * zero, its sign is the same as the sign of the first argument.
   * Special cases:
   * <ul><li>If either argument is NaN, or the first argument is infinite,
   * or the second argument is positive zero or negative zero, then the
   * result is NaN.
   * <li>If the first argument is finite and the second argument is
   * infinite, then the result is the same as the first argument.</ul>
   *
   * @param f1 the dividend.
   * @param f2 the divisor.
   * @return the remainder when {@code f1} is divided by {@code f2}.
   */
  public static native double IEEEremainder(double f1, double f2);

  /**
   * Returns the smallest (closest to negative infinity)
   * {@code double} value that is greater than or equal to the
   * argument and is equal to a mathematical integer. Special cases:
   * <ul><li>If the argument value is already equal to a
   * mathematical integer, then the result is the same as the
   * argument.  <li>If the argument is NaN or an infinity or
   * positive zero or negative zero, then the result is the same as
   * the argument.  <li>If the argument value is less than zero but
   * greater than -1.0, then the result is negative zero.</ul> Note
   * that the value of {@code StrictMath.ceil(x)} is exactly the
   * value of {@code -StrictMath.floor(-x)}.
   *
   * @param a a value.
   * @return the smallest (closest to negative infinity) floating-point value that is greater than
   * or equal to the argument and is equal to a mathematical integer.
   */
  public static double ceil(double a) {
    return floorOrCeil(a, -0.0, 1.0, 1.0);
  }

  /**
   * Returns the largest (closest to positive infinity)
   * {@code double} value that is less than or equal to the
   * argument and is equal to a mathematical integer. Special cases:
   * <ul><li>If the argument value is already equal to a
   * mathematical integer, then the result is the same as the
   * argument.  <li>If the argument is NaN or an infinity or
   * positive zero or negative zero, then the result is the same as
   * the argument.</ul>
   *
   * @param a a value.
   * @return the largest (closest to positive infinity) floating-point value that less than or equal
   * to the argument and is equal to a mathematical integer.
   */
  public static double floor(double a) {
    return floorOrCeil(a, -1.0, 0.0, -1.0);
  }

  /**
   * Internal method to share logic between floor and ceil.
   *
   * @param a the value to be floored or ceiled
   * @param negativeBoundary result for values in (-1, 0)
   * @param positiveBoundary result for values in (0, 1)
   * @param increment value to add when the argument is non-integral
   */
  private static double floorOrCeil(double a,
      double negativeBoundary,
      double positiveBoundary,
      double sign) {
    int exponent = Math.getExponent(a);

    if (exponent < 0) {
            /*
             * Absolute value of argument is less than 1.
             * floorOrceil(-0.0) => -0.0
             * floorOrceil(+0.0) => +0.0
             */
      return ((a == 0.0) ? a :
          ((a < 0.0) ? negativeBoundary : positiveBoundary));
    } else if (exponent >= 52) {
            /*
             * Infinity, NaN, or a value so large it must be integral.
             */
      return a;
    }
    // Else the argument is either an integral value already XOR it
    // has to be rounded to one.
    assert exponent >= 0 && exponent <= 51;

    long doppel = Double.doubleToRawLongBits(a);
    long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;

    if ((mask & doppel) == 0L) {
      return a; // integral value
    } else {
      double result = Double.longBitsToDouble(doppel & (~mask));
      if (sign * a > 0.0) {
        result = result + sign;
      }
      return result;
    }
  }

  /**
   * Returns the {@code double} value that is closest in value
   * to the argument and is equal to a mathematical integer. If two
   * {@code double} values that are mathematical integers are
   * equally close to the value of the argument, the result is the
   * integer value that is even. Special cases:
   * <ul><li>If the argument value is already equal to a mathematical
   * integer, then the result is the same as the argument.
   * <li>If the argument is NaN or an infinity or positive zero or negative
   * zero, then the result is the same as the argument.</ul>
   *
   * @param a a value.
   * @return the closest floating-point value to {@code a} that is equal to a mathematical integer.
   * @author Joseph D. Darcy
   */
  public static double rint(double a) {
        /*
         * If the absolute value of a is not less than 2^52, it
         * is either a finite integer (the double format does not have
         * enough significand bits for a number that large to have any
         * fractional portion), an infinity, or a NaN.  In any of
         * these cases, rint of the argument is the argument.
         *
         * Otherwise, the sum (twoToThe52 + a ) will properly round
         * away any fractional portion of a since ulp(twoToThe52) ==
         * 1.0; subtracting out twoToThe52 from this sum will then be
         * exact and leave the rounded integer portion of a.
         *
         * This method does *not* need to be declared strictfp to get
         * fully reproducible results.  Whether or not a method is
         * declared strictfp can only make a difference in the
         * returned result if some operation would overflow or
         * underflow with strictfp semantics.  The operation
         * (twoToThe52 + a ) cannot overflow since large values of a
         * are screened out; the add cannot underflow since twoToThe52
         * is too large.  The subtraction ((twoToThe52 + a ) -
         * twoToThe52) will be exact as discussed above and thus
         * cannot overflow or meaningfully underflow.  Finally, the
         * last multiply in the return statement is by plus or minus
         * 1.0, which is exact too.
         */
    double twoToThe52 = (double) (1L << 52); // 2^52
    double sign = Math.copySign(1.0, a); // preserve sign info
    a = Math.abs(a);

    if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
      a = ((twoToThe52 + a) - twoToThe52);
    }

    return sign * a; // restore original sign
  }

  /**
   * Returns the angle <i>theta</i> from the conversion of rectangular
   * coordinates ({@code x},&nbsp;{@code y}) to polar
   * coordinates (r,&nbsp;<i>theta</i>).
   * This method computes the phase <i>theta</i> by computing an arc tangent
   * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
   * cases:
   * <ul><li>If either argument is NaN, then the result is NaN.
   * <li>If the first argument is positive zero and the second argument
   * is positive, or the first argument is positive and finite and the
   * second argument is positive infinity, then the result is positive
   * zero.
   * <li>If the first argument is negative zero and the second argument
   * is positive, or the first argument is negative and finite and the
   * second argument is positive infinity, then the result is negative zero.
   * <li>If the first argument is positive zero and the second argument
   * is negative, or the first argument is positive and finite and the
   * second argument is negative infinity, then the result is the
   * {@code double} value closest to <i>pi</i>.
   * <li>If the first argument is negative zero and the second argument
   * is negative, or the first argument is negative and finite and the
   * second argument is negative infinity, then the result is the
   * {@code double} value closest to -<i>pi</i>.
   * <li>If the first argument is positive and the second argument is
   * positive zero or negative zero, or the first argument is positive
   * infinity and the second argument is finite, then the result is the
   * {@code double} value closest to <i>pi</i>/2.
   * <li>If the first argument is negative and the second argument is
   * positive zero or negative zero, or the first argument is negative
   * infinity and the second argument is finite, then the result is the
   * {@code double} value closest to -<i>pi</i>/2.
   * <li>If both arguments are positive infinity, then the result is the
   * {@code double} value closest to <i>pi</i>/4.
   * <li>If the first argument is positive infinity and the second argument
   * is negative infinity, then the result is the {@code double}
   * value closest to 3*<i>pi</i>/4.
   * <li>If the first argument is negative infinity and the second argument
   * is positive infinity, then the result is the {@code double} value
   * closest to -<i>pi</i>/4.
   * <li>If both arguments are negative infinity, then the result is the
   * {@code double} value closest to -3*<i>pi</i>/4.</ul>
   *
   * @param y the ordinate coordinate
   * @param x the abscissa coordinate
   * @return the <i>theta</i> component of the point (<i>r</i>,&nbsp;<i>theta</i>) in polar
   * coordinates that corresponds to the point (<i>x</i>,&nbsp;<i>y</i>) in Cartesian coordinates.
   */
  public static native double atan2(double y, double x);


  /**
   * Returns the value of the first argument raised to the power of the
   * second argument. Special cases:
   *
   * <ul><li>If the second argument is positive or negative zero, then the
   * result is 1.0.
   * <li>If the second argument is 1.0, then the result is the same as the
   * first argument.
   * <li>If the second argument is NaN, then the result is NaN.
   * <li>If the first argument is NaN and the second argument is nonzero,
   * then the result is NaN.
   *
   * <li>If
   * <ul>
   * <li>the absolute value of the first argument is greater than 1
   * and the second argument is positive infinity, or
   * <li>the absolute value of the first argument is less than 1 and
   * the second argument is negative infinity,
   * </ul>
   * then the result is positive infinity.
   *
   * <li>If
   * <ul>
   * <li>the absolute value of the first argument is greater than 1 and
   * the second argument is negative infinity, or
   * <li>the absolute value of the
   * first argument is less than 1 and the second argument is positive
   * infinity,
   * </ul>
   * then the result is positive zero.
   *
   * <li>If the absolute value of the first argument equals 1 and the
   * second argument is infinite, then the result is NaN.
   *
   * <li>If
   * <ul>
   * <li>the first argument is positive zero and the second argument
   * is greater than zero, or
   * <li>the first argument is positive infinity and the second
   * argument is less than zero,
   * </ul>
   * then the result is positive zero.
   *
   * <li>If
   * <ul>
   * <li>the first argument is positive zero and the second argument
   * is less than zero, or
   * <li>the first argument is positive infinity and the second
   * argument is greater than zero,
   * </ul>
   * then the result is positive infinity.
   *
   * <li>If
   * <ul>
   * <li>the first argument is negative zero and the second argument
   * is greater than zero but not a finite odd integer, or
   * <li>the first argument is negative infinity and the second
   * argument is less than zero but not a finite odd integer,
   * </ul>
   * then the result is positive zero.
   *
   * <li>If
   * <ul>
   * <li>the first argument is negative zero and the second argument
   * is a positive finite odd integer, or
   * <li>the first argument is negative infinity and the second
   * argument is a negative finite odd integer,
   * </ul>
   * then the result is negative zero.
   *
   * <li>If
   * <ul>
   * <li>the first argument is negative zero and the second argument
   * is less than zero but not a finite odd integer, or
   * <li>the first argument is negative infinity and the second
   * argument is greater than zero but not a finite odd integer,
   * </ul>
   * then the result is positive infinity.
   *
   * <li>If
   * <ul>
   * <li>the first argument is negative zero and the second argument
   * is a negative finite odd integer, or
   * <li>the first argument is negative infinity and the second
   * argument is a positive finite odd integer,
   * </ul>
   * then the result is negative infinity.
   *
   * <li>If the first argument is finite and less than zero
   * <ul>
   * <li> if the second argument is a finite even integer, the
   * result is equal to the result of raising the absolute value of
   * the first argument to the power of the second argument
   *
   * <li>if the second argument is a finite odd integer, the result
   * is equal to the negative of the result of raising the absolute
   * value of the first argument to the power of the second
   * argument
   *
   * <li>if the second argument is finite and not an integer, then
   * the result is NaN.
   * </ul>
   *
   * <li>If both arguments are integers, then the result is exactly equal
   * to the mathematical result of raising the first argument to the power
   * of the second argument if that result can in fact be represented
   * exactly as a {@code double} value.</ul>
   *
   * <p>(In the foregoing descriptions, a floating-point value is
   * considered to be an integer if and only if it is finite and a
   * fixed point of the method {@link #ceil ceil} or,
   * equivalently, a fixed point of the method {@link #floor
   * floor}. A value is a fixed point of a one-argument
   * method if and only if the result of applying the method to the
   * value is equal to the value.)
   *
   * @param a base.
   * @param b the exponent.
   * @return the value {@code a}<sup>{@code b}</sup>.
   */
  public static native double pow(double a, double b);

  /**
   * Returns the closest {@code int} to the argument, with ties
   * rounding to positive infinity.
   *
   * <p>Special cases:
   * <ul><li>If the argument is NaN, the result is 0.
   * <li>If the argument is negative infinity or any value less than or
   * equal to the value of {@code Integer.MIN_VALUE}, the result is
   * equal to the value of {@code Integer.MIN_VALUE}.
   * <li>If the argument is positive infinity or any value greater than or
   * equal to the value of {@code Integer.MAX_VALUE}, the result is
   * equal to the value of {@code Integer.MAX_VALUE}.</ul>
   *
   * @param a a floating-point value to be rounded to an integer.
   * @return the value of the argument rounded to the nearest {@code int} value.
   * @see java.lang.Integer#MAX_VALUE
   * @see java.lang.Integer#MIN_VALUE
   */
  public static int round(float a) {
    return Math.round(a);
  }

  /**
   * Returns the closest {@code long} to the argument, with ties
   * rounding to positive infinity.
   *
   * <p>Special cases:
   * <ul><li>If the argument is NaN, the result is 0.
   * <li>If the argument is negative infinity or any value less than or
   * equal to the value of {@code Long.MIN_VALUE}, the result is
   * equal to the value of {@code Long.MIN_VALUE}.
   * <li>If the argument is positive infinity or any value greater than or
   * equal to the value of {@code Long.MAX_VALUE}, the result is
   * equal to the value of {@code Long.MAX_VALUE}.</ul>
   *
   * @param a a floating-point value to be rounded to a {@code long}.
   * @return the value of the argument rounded to the nearest {@code long} value.
   * @see java.lang.Long#MAX_VALUE
   * @see java.lang.Long#MIN_VALUE
   */
  public static long round(double a) {
    return Math.round(a);
  }

  private static final class RandomNumberGeneratorHolder {

    static final Random randomNumberGenerator = new Random();
  }

  /**
   * Returns a {@code double} value with a positive sign, greater
   * than or equal to {@code 0.0} and less than {@code 1.0}.
   * Returned values are chosen pseudorandomly with (approximately)
   * uniform distribution from that range.
   *
   * <p>When this method is first called, it creates a single new
   * pseudorandom-number generator, exactly as if by the expression
   *
   * <blockquote>{@code new java.util.Random()}</blockquote>
   *
   * This new pseudorandom-number generator is used thereafter for
   * all calls to this method and is used nowhere else.
   *
   * <p>This method is properly synchronized to allow correct use by
   * more than one thread. However, if many threads need to generate
   * pseudorandom numbers at a great rate, it may reduce contention
   * for each thread to have its own pseudorandom-number generator.
   *
   * @return a pseudorandom {@code double} greater than or equal to {@code 0.0} and less than {@code
   * 1.0}.
   * @see Random#nextDouble()
   */
  public static double random() {
    return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
  }

  /**
   * Returns the sum of its arguments,
   * throwing an exception if the result overflows an {@code int}.
   *
   * @param x the first value
   * @param y the second value
   * @return the result
   * @throws ArithmeticException if the result overflows an int
   * @see Math#addExact(int, int)
   * @since 1.8
   */
  public static int addExact(int x, int y) {
    return Math.addExact(x, y);
  }

  /**
   * Returns the sum of its arguments,
   * throwing an exception if the result overflows a {@code long}.
   *
   * @param x the first value
   * @param y the second value
   * @return the result
   * @throws ArithmeticException if the result overflows a long
   * @see Math#addExact(long, long)
   * @since 1.8
   */
  public static long addExact(long x, long y) {
    return Math.addExact(x, y);
  }

  /**
   * Returns the difference of the arguments,
   * throwing an exception if the result overflows an {@code int}.
   *
   * @param x the first value
   * @param y the second value to subtract from the first
   * @return the result
   * @throws ArithmeticException if the result overflows an int
   * @see Math#subtractExact(int, int)
   * @since 1.8
   */
  public static int subtractExact(int x, int y) {
    return Math.subtractExact(x, y);
  }

  /**
   * Returns the difference of the arguments,
   * throwing an exception if the result overflows a {@code long}.
   *
   * @param x the first value
   * @param y the second value to subtract from the first
   * @return the result
   * @throws ArithmeticException if the result overflows a long
   * @see Math#subtractExact(long, long)
   * @since 1.8
   */
  public static long subtractExact(long x, long y) {
    return Math.subtractExact(x, y);
  }

  /**
   * Returns the product of the arguments,
   * throwing an exception if the result overflows an {@code int}.
   *
   * @param x the first value
   * @param y the second value
   * @return the result
   * @throws ArithmeticException if the result overflows an int
   * @see Math#multiplyExact(int, int)
   * @since 1.8
   */
  public static int multiplyExact(int x, int y) {
    return Math.multiplyExact(x, y);
  }

  /**
   * Returns the product of the arguments,
   * throwing an exception if the result overflows a {@code long}.
   *
   * @param x the first value
   * @param y the second value
   * @return the result
   * @throws ArithmeticException if the result overflows a long
   * @see Math#multiplyExact(long, long)
   * @since 1.8
   */
  public static long multiplyExact(long x, long y) {
    return Math.multiplyExact(x, y);
  }

  /**
   * Returns the value of the {@code long} argument;
   * throwing an exception if the value overflows an {@code int}.
   *
   * @param value the long value
   * @return the argument as an int
   * @throws ArithmeticException if the {@code argument} overflows an int
   * @see Math#toIntExact(long)
   * @since 1.8
   */
  public static int toIntExact(long value) {
    return Math.toIntExact(value);
  }

  /**
   * Returns the largest (closest to positive infinity)
   * {@code int} value that is less than or equal to the algebraic quotient.
   * There is one special case, if the dividend is the
   * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
   * then integer overflow occurs and
   * the result is equal to the {@code Integer.MIN_VALUE}.
   * <p>
   * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
   * a comparison to the integer division {@code /} operator.
   *
   * @param x the dividend
   * @param y the divisor
   * @return the largest (closest to positive infinity) {@code int} value that is less than or equal
   * to the algebraic quotient.
   * @throws ArithmeticException if the divisor {@code y} is zero
   * @see Math#floorDiv(int, int)
   * @see Math#floor(double)
   * @since 1.8
   */
  public static int floorDiv(int x, int y) {
    return Math.floorDiv(x, y);
  }

  /**
   * Returns the largest (closest to positive infinity)
   * {@code long} value that is less than or equal to the algebraic quotient.
   * There is one special case, if the dividend is the
   * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
   * then integer overflow occurs and
   * the result is equal to the {@code Long.MIN_VALUE}.
   * <p>
   * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
   * a comparison to the integer division {@code /} operator.
   *
   * @param x the dividend
   * @param y the divisor
   * @return the largest (closest to positive infinity) {@code long} value that is less than or
   * equal to the algebraic quotient.
   * @throws ArithmeticException if the divisor {@code y} is zero
   * @see Math#floorDiv(long, long)
   * @see Math#floor(double)
   * @since 1.8
   */
  public static long floorDiv(long x, long y) {
    return Math.floorDiv(x, y);
  }

  /**
   * Returns the floor modulus of the {@code int} arguments.
   * <p>
   * The floor modulus is {@code x - (floorDiv(x, y) * y)},
   * has the same sign as the divisor {@code y}, and
   * is in the range of {@code -abs(y) < r < +abs(y)}.
   * <p>
   * The relationship between {@code floorDiv} and {@code floorMod} is such that:
   * <ul>
   * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
   * </ul>
   * <p>
   * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
   * a comparison to the {@code %} operator.
   *
   * @param x the dividend
   * @param y the divisor
   * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
   * @throws ArithmeticException if the divisor {@code y} is zero
   * @see Math#floorMod(int, int)
   * @see StrictMath#floorDiv(int, int)
   * @since 1.8
   */
  public static int floorMod(int x, int y) {
    return Math.floorMod(x, y);
  }

  /**
   * Returns the floor modulus of the {@code long} arguments.
   * <p>
   * The floor modulus is {@code x - (floorDiv(x, y) * y)},
   * has the same sign as the divisor {@code y}, and
   * is in the range of {@code -abs(y) < r < +abs(y)}.
   * <p>
   * The relationship between {@code floorDiv} and {@code floorMod} is such that:
   * <ul>
   * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
   * </ul>
   * <p>
   * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
   * a comparison to the {@code %} operator.
   *
   * @param x the dividend
   * @param y the divisor
   * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
   * @throws ArithmeticException if the divisor {@code y} is zero
   * @see Math#floorMod(long, long)
   * @see StrictMath#floorDiv(long, long)
   * @since 1.8
   */
  public static long floorMod(long x, long y) {
    return Math.floorMod(x, y);
  }

  /**
   * Returns the absolute value of an {@code int} value.
   * If the argument is not negative, the argument is returned.
   * If the argument is negative, the negation of the argument is returned.
   *
   * <p>Note that if the argument is equal to the value of
   * {@link Integer#MIN_VALUE}, the most negative representable
   * {@code int} value, the result is that same value, which is
   * negative.
   *
   * @param a the  argument whose absolute value is to be determined.
   * @return the absolute value of the argument.
   */
  public static int abs(int a) {
    return Math.abs(a);
  }

  /**
   * Returns the absolute value of a {@code long} value.
   * If the argument is not negative, the argument is returned.
   * If the argument is negative, the negation of the argument is returned.
   *
   * <p>Note that if the argument is equal to the value of
   * {@link Long#MIN_VALUE}, the most negative representable
   * {@code long} value, the result is that same value, which
   * is negative.
   *
   * @param a the  argument whose absolute value is to be determined.
   * @return the absolute value of the argument.
   */
  public static long abs(long a) {
    return Math.abs(a);
  }

  /**
   * Returns the absolute value of a {@code float} value.
   * If the argument is not negative, the argument is returned.
   * If the argument is negative, the negation of the argument is returned.
   * Special cases:
   * <ul><li>If the argument is positive zero or negative zero, the
   * result is positive zero.
   * <li>If the argument is infinite, the result is positive infinity.
   * <li>If the argument is NaN, the result is NaN.</ul>
   * In other words, the result is the same as the value of the expression:
   * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
   *
   * @param a the argument whose absolute value is to be determined
   * @return the absolute value of the argument.
   */
  public static float abs(float a) {
    return Math.abs(a);
  }

  /**
   * Returns the absolute value of a {@code double} value.
   * If the argument is not negative, the argument is returned.
   * If the argument is negative, the negation of the argument is returned.
   * Special cases:
   * <ul><li>If the argument is positive zero or negative zero, the result
   * is positive zero.
   * <li>If the argument is infinite, the result is positive infinity.
   * <li>If the argument is NaN, the result is NaN.</ul>
   * In other words, the result is the same as the value of the expression:
   * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
   *
   * @param a the argument whose absolute value is to be determined
   * @return the absolute value of the argument.
   */
  public static double abs(double a) {
    return Math.abs(a);
  }

  /**
   * Returns the greater of two {@code int} values. That is, the
   * result is the argument closer to the value of
   * {@link Integer#MAX_VALUE}. If the arguments have the same value,
   * the result is that same value.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the larger of {@code a} and {@code b}.
   */
  public static int max(int a, int b) {
    return Math.max(a, b);
  }

  /**
   * Returns the greater of two {@code long} values. That is, the
   * result is the argument closer to the value of
   * {@link Long#MAX_VALUE}. If the arguments have the same value,
   * the result is that same value.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the larger of {@code a} and {@code b}.
   */
  public static long max(long a, long b) {
    return Math.max(a, b);
  }

  /**
   * Returns the greater of two {@code float} values.  That is,
   * the result is the argument closer to positive infinity. If the
   * arguments have the same value, the result is that same
   * value. If either value is NaN, then the result is NaN.  Unlike
   * the numerical comparison operators, this method considers
   * negative zero to be strictly smaller than positive zero. If one
   * argument is positive zero and the other negative zero, the
   * result is positive zero.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the larger of {@code a} and {@code b}.
   */
  public static float max(float a, float b) {
    return Math.max(a, b);
  }

  /**
   * Returns the greater of two {@code double} values.  That
   * is, the result is the argument closer to positive infinity. If
   * the arguments have the same value, the result is that same
   * value. If either value is NaN, then the result is NaN.  Unlike
   * the numerical comparison operators, this method considers
   * negative zero to be strictly smaller than positive zero. If one
   * argument is positive zero and the other negative zero, the
   * result is positive zero.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the larger of {@code a} and {@code b}.
   */
  public static double max(double a, double b) {
    return Math.max(a, b);
  }

  /**
   * Returns the smaller of two {@code int} values. That is,
   * the result the argument closer to the value of
   * {@link Integer#MIN_VALUE}.  If the arguments have the same
   * value, the result is that same value.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the smaller of {@code a} and {@code b}.
   */
  public static int min(int a, int b) {
    return Math.min(a, b);
  }

  /**
   * Returns the smaller of two {@code long} values. That is,
   * the result is the argument closer to the value of
   * {@link Long#MIN_VALUE}. If the arguments have the same
   * value, the result is that same value.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the smaller of {@code a} and {@code b}.
   */
  public static long min(long a, long b) {
    return Math.min(a, b);
  }

  /**
   * Returns the smaller of two {@code float} values.  That is,
   * the result is the value closer to negative infinity. If the
   * arguments have the same value, the result is that same
   * value. If either value is NaN, then the result is NaN.  Unlike
   * the numerical comparison operators, this method considers
   * negative zero to be strictly smaller than positive zero.  If
   * one argument is positive zero and the other is negative zero,
   * the result is negative zero.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the smaller of {@code a} and {@code b.}
   */
  public static float min(float a, float b) {
    return Math.min(a, b);
  }

  /**
   * Returns the smaller of two {@code double} values.  That
   * is, the result is the value closer to negative infinity. If the
   * arguments have the same value, the result is that same
   * value. If either value is NaN, then the result is NaN.  Unlike
   * the numerical comparison operators, this method considers
   * negative zero to be strictly smaller than positive zero. If one
   * argument is positive zero and the other is negative zero, the
   * result is negative zero.
   *
   * @param a an argument.
   * @param b another argument.
   * @return the smaller of {@code a} and {@code b}.
   */
  public static double min(double a, double b) {
    return Math.min(a, b);
  }

  /**
   * Returns the size of an ulp of the argument.  An ulp, unit in
   * the last place, of a {@code double} value is the positive
   * distance between this floating-point value and the {@code
   * double} value next larger in magnitude.  Note that for non-NaN
   * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, then the result is NaN.
   * <li> If the argument is positive or negative infinity, then the
   * result is positive infinity.
   * <li> If the argument is positive or negative zero, then the result is
   * {@code Double.MIN_VALUE}.
   * <li> If the argument is &plusmn;{@code Double.MAX_VALUE}, then
   * the result is equal to 2<sup>971</sup>.
   * </ul>
   *
   * @param d the floating-point value whose ulp is to be returned
   * @return the size of an ulp of the argument
   * @author Joseph D. Darcy
   * @since 1.5
   */
  public static double ulp(double d) {
    return Math.ulp(d);
  }

  /**
   * Returns the size of an ulp of the argument.  An ulp, unit in
   * the last place, of a {@code float} value is the positive
   * distance between this floating-point value and the {@code
   * float} value next larger in magnitude.  Note that for non-NaN
   * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, then the result is NaN.
   * <li> If the argument is positive or negative infinity, then the
   * result is positive infinity.
   * <li> If the argument is positive or negative zero, then the result is
   * {@code Float.MIN_VALUE}.
   * <li> If the argument is &plusmn;{@code Float.MAX_VALUE}, then
   * the result is equal to 2<sup>104</sup>.
   * </ul>
   *
   * @param f the floating-point value whose ulp is to be returned
   * @return the size of an ulp of the argument
   * @author Joseph D. Darcy
   * @since 1.5
   */
  public static float ulp(float f) {
    return Math.ulp(f);
  }

  /**
   * Returns the signum function of the argument; zero if the argument
   * is zero, 1.0 if the argument is greater than zero, -1.0 if the
   * argument is less than zero.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, then the result is NaN.
   * <li> If the argument is positive zero or negative zero, then the
   * result is the same as the argument.
   * </ul>
   *
   * @param d the floating-point value whose signum is to be returned
   * @return the signum function of the argument
   * @author Joseph D. Darcy
   * @since 1.5
   */
  public static double signum(double d) {
    return Math.signum(d);
  }

  /**
   * Returns the signum function of the argument; zero if the argument
   * is zero, 1.0f if the argument is greater than zero, -1.0f if the
   * argument is less than zero.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, then the result is NaN.
   * <li> If the argument is positive zero or negative zero, then the
   * result is the same as the argument.
   * </ul>
   *
   * @param f the floating-point value whose signum is to be returned
   * @return the signum function of the argument
   * @author Joseph D. Darcy
   * @since 1.5
   */
  public static float signum(float f) {
    return Math.signum(f);
  }

  /**
   * Returns the hyperbolic sine of a {@code double} value.
   * The hyperbolic sine of <i>x</i> is defined to be
   * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/2
   * where <i>e</i> is {@linkplain Math#E Euler's number}.
   *
   * <p>Special cases:
   * <ul>
   *
   * <li>If the argument is NaN, then the result is NaN.
   *
   * <li>If the argument is infinite, then the result is an infinity
   * with the same sign as the argument.
   *
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.
   *
   * </ul>
   *
   * @param x The number whose hyperbolic sine is to be returned.
   * @return The hyperbolic sine of {@code x}.
   * @since 1.5
   */
  public static native double sinh(double x);

  /**
   * Returns the hyperbolic cosine of a {@code double} value.
   * The hyperbolic cosine of <i>x</i> is defined to be
   * (<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>)/2
   * where <i>e</i> is {@linkplain Math#E Euler's number}.
   *
   * <p>Special cases:
   * <ul>
   *
   * <li>If the argument is NaN, then the result is NaN.
   *
   * <li>If the argument is infinite, then the result is positive
   * infinity.
   *
   * <li>If the argument is zero, then the result is {@code 1.0}.
   *
   * </ul>
   *
   * @param x The number whose hyperbolic cosine is to be returned.
   * @return The hyperbolic cosine of {@code x}.
   * @since 1.5
   */
  public static native double cosh(double x);

  /**
   * Returns the hyperbolic tangent of a {@code double} value. The hyperbolic tangent of <i>x</i> is
   * defined to be (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>),
   * in other words, {@linkplain Math#sinh sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}.
   * Note that the absolute value of the exact tanh is always less than 1.
   *
   * <p>Special cases: <ul>
   *
   * <li>If the argument is NaN, then the result is NaN.
   *
   * <li>If the argument is zero, then the result is a zero with the same sign as the argument.
   *
   * <li>If the argument is positive infinity, then the result is {@code +1.0}.
   *
   * <li>If the argument is negative infinity, then the result is {@code -1.0}.
   *
   * </ul>
   *
   * @param x The number whose hyperbolic tangent is to be returned.
   * @return The hyperbolic tangent of {@code x}.
   * @since 1.5
   */
  public static native double tanh(double x);

  /**
   * Returns sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
   * without intermediate overflow or underflow.
   *
   * <p>Special cases:
   * <ul>
   *
   * <li> If either argument is infinite, then the result
   * is positive infinity.
   *
   * <li> If either argument is NaN and neither argument is infinite,
   * then the result is NaN.
   *
   * </ul>
   *
   * @param x a value
   * @param y a value
   * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>) without intermediate overflow or
   * underflow
   * @since 1.5
   */
  public static native double hypot(double x, double y);

  /**
   * Returns <i>e</i><sup>x</sup>&nbsp;-1.  Note that for values of
   * <i>x</i> near 0, the exact sum of
   * {@code expm1(x)}&nbsp;+&nbsp;1 is much closer to the true
   * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
   *
   * <p>Special cases:
   * <ul>
   * <li>If the argument is NaN, the result is NaN.
   *
   * <li>If the argument is positive infinity, then the result is
   * positive infinity.
   *
   * <li>If the argument is negative infinity, then the result is
   * -1.0.
   *
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.
   *
   * </ul>
   *
   * @param x the exponent to raise <i>e</i> to in the computation of <i>e</i><sup>{@code
   * x}</sup>&nbsp;-1.
   * @return the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1.
   * @since 1.5
   */
  public static native double expm1(double x);

  /**
   * Returns the natural logarithm of the sum of the argument and 1.
   * Note that for small values {@code x}, the result of
   * {@code log1p(x)} is much closer to the true result of ln(1
   * + {@code x}) than the floating-point evaluation of
   * {@code log(1.0+x)}.
   *
   * <p>Special cases:
   * <ul>
   *
   * <li>If the argument is NaN or less than -1, then the result is
   * NaN.
   *
   * <li>If the argument is positive infinity, then the result is
   * positive infinity.
   *
   * <li>If the argument is negative one, then the result is
   * negative infinity.
   *
   * <li>If the argument is zero, then the result is a zero with the
   * same sign as the argument.
   *
   * </ul>
   *
   * @param x a value
   * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural log of {@code x}&nbsp;+&nbsp;1
   * @since 1.5
   */
  public static native double log1p(double x);

  /**
   * Returns the first floating-point argument with the sign of the
   * second floating-point argument.  For this method, a NaN
   * {@code sign} argument is always treated as if it were
   * positive.
   *
   * @param magnitude the parameter providing the magnitude of the result
   * @param sign the parameter providing the sign of the result
   * @return a value with the magnitude of {@code magnitude} and the sign of {@code sign}.
   * @since 1.6
   */
  public static double copySign(double magnitude, double sign) {
    return Math.copySign(magnitude, (Double.isNaN(sign) ? 1.0d : sign));
  }

  /**
   * Returns the first floating-point argument with the sign of the
   * second floating-point argument.  For this method, a NaN
   * {@code sign} argument is always treated as if it were
   * positive.
   *
   * @param magnitude the parameter providing the magnitude of the result
   * @param sign the parameter providing the sign of the result
   * @return a value with the magnitude of {@code magnitude} and the sign of {@code sign}.
   * @since 1.6
   */
  public static float copySign(float magnitude, float sign) {
    return Math.copySign(magnitude, (Float.isNaN(sign) ? 1.0f : sign));
  }

  /**
   * Returns the unbiased exponent used in the representation of a
   * {@code float}.  Special cases:
   *
   * <ul>
   * <li>If the argument is NaN or infinite, then the result is
   * {@link Float#MAX_EXPONENT} + 1.
   * <li>If the argument is zero or subnormal, then the result is
   * {@link Float#MIN_EXPONENT} -1.
   * </ul>
   *
   * @param f a {@code float} value
   * @return the unbiased exponent of the argument
   * @since 1.6
   */
  public static int getExponent(float f) {
    return Math.getExponent(f);
  }

  /**
   * Returns the unbiased exponent used in the representation of a
   * {@code double}.  Special cases:
   *
   * <ul>
   * <li>If the argument is NaN or infinite, then the result is
   * {@link Double#MAX_EXPONENT} + 1.
   * <li>If the argument is zero or subnormal, then the result is
   * {@link Double#MIN_EXPONENT} -1.
   * </ul>
   *
   * @param d a {@code double} value
   * @return the unbiased exponent of the argument
   * @since 1.6
   */
  public static int getExponent(double d) {
    return Math.getExponent(d);
  }

  /**
   * Returns the floating-point number adjacent to the first
   * argument in the direction of the second argument.  If both
   * arguments compare as equal the second argument is returned.
   *
   * <p>Special cases:
   * <ul>
   * <li> If either argument is a NaN, then NaN is returned.
   *
   * <li> If both arguments are signed zeros, {@code direction}
   * is returned unchanged (as implied by the requirement of
   * returning the second argument if the arguments compare as
   * equal).
   *
   * <li> If {@code start} is
   * &plusmn;{@link Double#MIN_VALUE} and {@code direction}
   * has a value such that the result should have a smaller
   * magnitude, then a zero with the same sign as {@code start}
   * is returned.
   *
   * <li> If {@code start} is infinite and
   * {@code direction} has a value such that the result should
   * have a smaller magnitude, {@link Double#MAX_VALUE} with the
   * same sign as {@code start} is returned.
   *
   * <li> If {@code start} is equal to &plusmn;
   * {@link Double#MAX_VALUE} and {@code direction} has a
   * value such that the result should have a larger magnitude, an
   * infinity with same sign as {@code start} is returned.
   * </ul>
   *
   * @param start starting floating-point value
   * @param direction value indicating which of {@code start}'s neighbors or {@code start} should be
   * returned
   * @return The floating-point number adjacent to {@code start} in the direction of {@code
   * direction}.
   * @since 1.6
   */
  public static double nextAfter(double start, double direction) {
    return Math.nextAfter(start, direction);
  }

  /**
   * Returns the floating-point number adjacent to the first
   * argument in the direction of the second argument.  If both
   * arguments compare as equal a value equivalent to the second argument
   * is returned.
   *
   * <p>Special cases:
   * <ul>
   * <li> If either argument is a NaN, then NaN is returned.
   *
   * <li> If both arguments are signed zeros, a value equivalent
   * to {@code direction} is returned.
   *
   * <li> If {@code start} is
   * &plusmn;{@link Float#MIN_VALUE} and {@code direction}
   * has a value such that the result should have a smaller
   * magnitude, then a zero with the same sign as {@code start}
   * is returned.
   *
   * <li> If {@code start} is infinite and
   * {@code direction} has a value such that the result should
   * have a smaller magnitude, {@link Float#MAX_VALUE} with the
   * same sign as {@code start} is returned.
   *
   * <li> If {@code start} is equal to &plusmn;
   * {@link Float#MAX_VALUE} and {@code direction} has a
   * value such that the result should have a larger magnitude, an
   * infinity with same sign as {@code start} is returned.
   * </ul>
   *
   * @param start starting floating-point value
   * @param direction value indicating which of {@code start}'s neighbors or {@code start} should be
   * returned
   * @return The floating-point number adjacent to {@code start} in the direction of {@code
   * direction}.
   * @since 1.6
   */
  public static float nextAfter(float start, double direction) {
    return Math.nextAfter(start, direction);
  }

  /**
   * Returns the floating-point value adjacent to {@code d} in
   * the direction of positive infinity.  This method is
   * semantically equivalent to {@code nextAfter(d,
   * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
   * implementation may run faster than its equivalent
   * {@code nextAfter} call.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, the result is NaN.
   *
   * <li> If the argument is positive infinity, the result is
   * positive infinity.
   *
   * <li> If the argument is zero, the result is
   * {@link Double#MIN_VALUE}
   *
   * </ul>
   *
   * @param d starting floating-point value
   * @return The adjacent floating-point value closer to positive infinity.
   * @since 1.6
   */
  public static double nextUp(double d) {
    return Math.nextUp(d);
  }

  /**
   * Returns the floating-point value adjacent to {@code f} in
   * the direction of positive infinity.  This method is
   * semantically equivalent to {@code nextAfter(f,
   * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
   * implementation may run faster than its equivalent
   * {@code nextAfter} call.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, the result is NaN.
   *
   * <li> If the argument is positive infinity, the result is
   * positive infinity.
   *
   * <li> If the argument is zero, the result is
   * {@link Float#MIN_VALUE}
   *
   * </ul>
   *
   * @param f starting floating-point value
   * @return The adjacent floating-point value closer to positive infinity.
   * @since 1.6
   */
  public static float nextUp(float f) {
    return Math.nextUp(f);
  }

  /**
   * Returns the floating-point value adjacent to {@code d} in
   * the direction of negative infinity.  This method is
   * semantically equivalent to {@code nextAfter(d,
   * Double.NEGATIVE_INFINITY)}; however, a
   * {@code nextDown} implementation may run faster than its
   * equivalent {@code nextAfter} call.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, the result is NaN.
   *
   * <li> If the argument is negative infinity, the result is
   * negative infinity.
   *
   * <li> If the argument is zero, the result is
   * {@code -Double.MIN_VALUE}
   *
   * </ul>
   *
   * @param d starting floating-point value
   * @return The adjacent floating-point value closer to negative infinity.
   * @since 1.8
   */
  public static double nextDown(double d) {
    return Math.nextDown(d);
  }

  /**
   * Returns the floating-point value adjacent to {@code f} in
   * the direction of negative infinity.  This method is
   * semantically equivalent to {@code nextAfter(f,
   * Float.NEGATIVE_INFINITY)}; however, a
   * {@code nextDown} implementation may run faster than its
   * equivalent {@code nextAfter} call.
   *
   * <p>Special Cases:
   * <ul>
   * <li> If the argument is NaN, the result is NaN.
   *
   * <li> If the argument is negative infinity, the result is
   * negative infinity.
   *
   * <li> If the argument is zero, the result is
   * {@code -Float.MIN_VALUE}
   *
   * </ul>
   *
   * @param f starting floating-point value
   * @return The adjacent floating-point value closer to negative infinity.
   * @since 1.8
   */
  public static float nextDown(float f) {
    return Math.nextDown(f);
  }

  /**
   * Returns {@code d} &times;
   * 2<sup>{@code scaleFactor}</sup> rounded as if performed
   * by a single correctly rounded floating-point multiply to a
   * member of the double value set.  See the Java
   * Language Specification for a discussion of floating-point
   * value sets.  If the exponent of the result is between {@link
   * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
   * answer is calculated exactly.  If the exponent of the result
   * would be larger than {@code Double.MAX_EXPONENT}, an
   * infinity is returned.  Note that if the result is subnormal,
   * precision may be lost; that is, when {@code scalb(x, n)}
   * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
   * <i>x</i>.  When the result is non-NaN, the result has the same
   * sign as {@code d}.
   *
   * <p>Special cases:
   * <ul>
   * <li> If the first argument is NaN, NaN is returned.
   * <li> If the first argument is infinite, then an infinity of the
   * same sign is returned.
   * <li> If the first argument is zero, then a zero of the same
   * sign is returned.
   * </ul>
   *
   * @param d number to be scaled by a power of two.
   * @param scaleFactor power of 2 used to scale {@code d}
   * @return {@code d} &times; 2<sup>{@code scaleFactor}</sup>
   * @since 1.6
   */
  public static double scalb(double d, int scaleFactor) {
    return Math.scalb(d, scaleFactor);
  }

  /**
   * Returns {@code f} &times;
   * 2<sup>{@code scaleFactor}</sup> rounded as if performed
   * by a single correctly rounded floating-point multiply to a
   * member of the float value set.  See the Java
   * Language Specification for a discussion of floating-point
   * value sets.  If the exponent of the result is between {@link
   * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
   * answer is calculated exactly.  If the exponent of the result
   * would be larger than {@code Float.MAX_EXPONENT}, an
   * infinity is returned.  Note that if the result is subnormal,
   * precision may be lost; that is, when {@code scalb(x, n)}
   * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
   * <i>x</i>.  When the result is non-NaN, the result has the same
   * sign as {@code f}.
   *
   * <p>Special cases:
   * <ul>
   * <li> If the first argument is NaN, NaN is returned.
   * <li> If the first argument is infinite, then an infinity of the
   * same sign is returned.
   * <li> If the first argument is zero, then a zero of the same
   * sign is returned.
   * </ul>
   *
   * @param f number to be scaled by a power of two.
   * @param scaleFactor power of 2 used to scale {@code f}
   * @return {@code f} &times; 2<sup>{@code scaleFactor}</sup>
   * @since 1.6
   */
  public static float scalb(float f, int scaleFactor) {
    return Math.scalb(f, scaleFactor);
  }
}
